CBSE Class 10 Mathematics Arithmetic Progression MCQs Set D

Question. For the A.P. a + (a + d) + (a + 2d) + .... + l of n terms :-
(a) S_n = n/ 2 (a + l)
(b) S_n = n/ 2 {2a + (n−1) d}
(c) S_n = n /2 {2l − (n−1) d}
(d) All of the options

Answer: D

Question. If a, b, c are in A.P. then :-
(a) the equation (b − c) x² + (c − a) x + (a − b) = 0, b ≠ c has equal roots
(b) a², b², c² are in A.P.
(c) λa + µ, λb + µ, lc + µ are in A.P., λ, µ ∈ R
(d) None of the options

Answer: A, C

Question. A person pays Rs. 975 in monthly instalments, each monthly instalment being less than the former by Rs. 5. The amount of the first instalment is Rs. 100. In what tune, will the entire amount be paid ?
(a) 12 months
(b) 26 months
(c) 15 months
(d) 18 months

Answer: C

Question. If the sum of first n terms of an A.P. is Pn + Qn² where P and Q are constants, then common difference of A.P. will be :-
(a) P + Q
(b) P − Q
(c) 2P
(d) 2Q

Answer: D

Question. In an A.P. sum of first p terms is equal to the sum of first q terms. Sum of it's first p + q terms is :-
(a) − (p + q)
(b) p + q
(c) 0
(d) None

Answer: C

Question. The first term of an AP is p and the common difference is q, then its 10th term is
(a) q + 9p
(b) p – 9q
(c) p + 9q
(d) 2p + 9p

Answer: C

Question. If the nth term of an A.P. is 4n + 1, then the common difference is
(a) 3
(b) 4
(c) 5
(d) 6

Answer: B

Question. 30 trees are planted in a straight line at intervals of 5 m. To water them, the gardener needs to bring water for each tree, separately from a well, which is 10 m from the first tree in line with the trees. How far will he have to walk in order to water all the trees beginnings with the first tree ? Assume that he starts from the well.
(a) 4785 m
(b) 4795 m
(c) 4800 m
(d) None of the options

Answer: B

Question. In an A.P., sum of first n terms is 2n² + 3n, it's common difference is :-
(a) 4
(b) 3
(c) 2
(d) 6

Answer: A

Question. The sum of all numbers from 1 to 1000 which are neither divisible by 2 nor by 5 is :-
(a) 200000
(b) 500500
(c) 250000
(d) None of the options

Answer: A

Question. If the angles A < B < C of a triangle are in A.P. then :-
(a) c² = a² + b² − ab
(b) b² = a2 + c² − ac
(c) c² = a² + b²
(d) None of the options

Answer: C

Question. A man arranged to pay off a debt of Rs.3600 in 40 annual instalments which form an Arithmetical Progression. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the 1 instalment is
(a) Rs.55
(b) Rs.53
(c) Rs.51
(d) Rs.49

Answer: C

Question. If a_n = 5n – 4 is a sequence, then a₁₂ is
(a) 48
(b) 52
(c) 56
(d) 62

Answer: C

Question. If a_n = 3n – 2, then the value of a₇ + a₈ is
(a) 39
(b) 41
(c) 47
(d) 53

Answer: B

Question. Let a₁, a₂,.......a19 be the first 19 terms of an arithmetic progression where a₁+a₈+a₁₂+a₁₉=224. The sum a₁ + a₂+ a₃ +...+a₁₉ is equal to
(a) 896
(b) 969
(c) 1064
(d) 1120

Answer: C

Question. Given that n A.M.'s are inserted between two sets of numbers a, 2b and 2a, b, where a, b Î R. If the mth means in the two cases are same then ratio a : b is equal to :-
(a) n : (n − m + 1)
(b) (n − m + 1) : m
(c) (n − m + 1) : n
(d) m : (n − m + 1)

Answer: D

Question. The value of n, for which aⁿ⁺¹ +bⁿ⁺¹/aⁿ +bⁿ is the A.M. between a and b is :-
(a) 0
(b) 1
(c) − 1/ 2
(d) −1

Answer: A

Question. For an A.P., kn n S S is independent of n. The value of d a for this A.P. is :-
(a) 1
(b) 2
(c) 3
(d) 4

Answer: C

Question. The n^th term of the AP: a, 3a, 5a, ... is
(a) na
(b) (2n – 1)a
(c) (2n + 1)a
(d) 2na

Answer: B

Question. If the sum to n terms of an AP is 3n² + 4n, then the common difference of the AP is
(a) 7
(b) 5
(c) 8
(d) 6

Answer: D

Question. The n^th term of the sequence 2, 5, 11, 20, 32, ............. is :-
(a) 3n²+3n−4/2
(b) 3n²+3n+4/2
(c) 3n²+3n+4/2
(d) None of the options

Answer: B

Question. A club consists of members whose ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old andhe sum of the ages of all the members is 250 year, then the number of members in the club are
(a) 15
(b) 20
(c) 25
(d) 30

Answer: C

Question. In an AP, if d = – 4, n = 7, an = 4, then a is
(a) 6
(b) 7
(c) 20
(d) 28

Answer: D

Question. If the first term of an AP is 1 and the common difference is 2, then the sum of first 26 terms is
(a) 484
(b) 576
(c) 676
(d) 625

Answer: C

Question. The sum of first n terms of an A.P. whose last term is l and common difference is d is :-
(a) n/ 2 [2l + (n − 1) d]
(b) n/ 2 [2l − (n − 1) d]
(c) n/ 2 [l + (n − 1) d]
(d) n /2 [l − (n − 1) d]

Answer: B

Question. If the sides of a right triangle are in A.P., then the ratio of its smallest side to the greatest side is :-
(a) 3 : 4
(b) 3 : 5
(c) 4 : 5
(d) None

Answer: C

Question. Sum of first n terms of an A.P. is an(n − 1). The sum of squares of these terms is :-
(a) a²/ 6 n(n − 1) (2n − 1)
(b) 2a²/ 3 n(n + 1) (2n + 1)
(c) a²n²(n − 1)²
(d) 2a² /3 n(n − 1) (2n − 1)

Answer: D

Question. If x, y, z are in A.P., then (x + 2y − z) (x + z − y) (z + 2y − x) is equal to :-
(a) xyz
(b) 2xyz
(c) 4xyz
(d) None

Answer: C

Question. The second term of the sequence defined by a_n = 3n + 2 is
(a) 2
(b) 4
(c) 6
(d) 8

Answer: D

Question. If 4/5 , a, 2 are three consecutive terms of an AP, then the value of a is
(a) 5/2
(b) 2/7
(c) 5/7
(d) 7/5

Answer: A

Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Common difference of the AP: –5, –1, 3, 7, ... is 4.
Reason (R): Common difference of the AP : a, a + d, a + 2d, ... is given by d = 2^nd term – 1^st term.

Answer: A

Question. Assertion (A): If nth term of an AP is 7 – 4n, then its common difference is – 4.
Reason (R): Common difference of an AP is given by d = aⁿ⁺¹ – an.

Answer: A

Question. Assertion (A): Common difference of an AP in which a₂₁ – a₇ = 84 is 14.
Reason (R): nth term of an AP is given by a_n = a + (n – 1) d.

Answer: D

Question. Assertion (A): The arrangement of numbers, i.e., – 4, 16, – 64, 256, – 1024, 4096, ... form a sequence.
Reason (R): An arrangement of numbers which are arranged in a definite order according to some rule, is called a sequence.

Answer: A

Question. Assertion (A): Sequence 1, 5, 9, 13, 17, 21, ... is a finite sequence.
Reason (R): A sequence with finite number of terms or numbers is called a finite sequence

Answer: D